The relation between magnetic moment ( M ) of a current carrying circular coil and length (L) of the wire used is

Step-by-step solution

The magnetic moment of a circular coil with N turns carrying current I is expressed as M = NIA , where A = r^2 is the area per turn. Given a fixed wire length L = N(2 r) , the radius is determined by r = L 2 N . Substituting into the area formula yields A = ( L 2 N )^2 = L^2 4 N^2 . Thus, the magnetic moment becomes M = NI L^2 4 N^2 = I L^2 4 N . For constant I and N , M L^2 , indicating direct proportionality to the square of the wire length. The correct choice is C .